I was wondering if one needed to prove principles. E.g., likelihood or condionality principles in Stats.
Thank you!
Asked
Active
Viewed 72 times
1 Answers
0
All non-axioms should be proved, in any area of mathematics or logic, always. Put another way: a statement assumed without proof is an "axiom", and hence "principles" should always be proved (or they would be called "axioms" instead!), although they are usually called "principles" because they are very basic and learned right away when studying a subject. Two good examples that come to mind are the Pigeonhole Principle or Principle of Inclusion-Exclusion in combinatorics.
Although, if you're asking whether you should always prove the principles you use, that depends heavily on context. You should be able to, but in publications, for example, or on a much larger problem, I wouldn't stop to prove the Principle of Inclusion-Exclusion, as an example.
I hope this helps!
The Count
- 3,620
-
The likelihood principle is rather different to your examples – Henry Jul 02 '16 at 23:32
-
I don't disagree. I just gave examples. – The Count Jul 02 '16 at 23:35
-
@Нenry:so would you say tНat the likeliНood principle or condionality principles are like axioms or still like the Principle of Inclusion-Exclusion in Count's example? – Lola Jul 03 '16 at 07:06
-
@The Count:so would you say tНat the likeliНood principle or condionality principles are like axioms or still like the Principle of Inclusion-Exclusion in your example? – Lola Sep 30 '16 at 12:24
-
@Lola I will freely admit that I do not understand or know enough about the Likelihood Principle or Conditionality Principles. Having looked briefly at a few books, I think perhaps I was a bit rigid in my original answer. A "principle" isn't such a rigidly defined word. Inclusion-Exclusion is a thing to be proved, but it seems as though the likelihood principle is more axiomatic. That is just my sense as a non-expert in statistics, though. I encourage you to seek lots of different opinions! – The Count Sep 30 '16 at 14:23